Pithoprakta: The historical measures 52-59: New evidence in glissando speed formalization Theory & theoretical applications

Assimilating glissandos to monatomic gas molecular movements and considering that molecular speeds are proportional to molecular mean kinetic energy (temperature), Xenakis seeks for normal distributions of sound speeds (glissandos) via Gauss equation. He uses a two-variable form of the equation (bi-dimensional domains) and then a three-variable one (three-dimensional domains). Through correlation he proves that speed distributions provided by both forms of Gauss equation are practically equivalent. Thus, temperature might be resulting from glissando execution limitations, i.e. speed limits. Since mean speed value becomes an invariable, temperature is meant to be a logically designated magnitude. Consequently, the introduction of speed as a scientific notion in composition is justified. Given that glissando directions are not stochastically preset, probabilistic determinism controls the interior of the sound mass, meas. 52-59, but not its overall evolving form. After having set all required parameters, Xenakis draws a general probability table that leads to 33 analytical sub-tables; 1168 theoretical and 1221 effective speeds are provided and virtually distributed to bowed instruments. Yet, both numbers remain theoretical as the majority of speeds are too quick for execution. A more realistic eventual maximum speed is applied then. Depending on speed, temperature is now close to “temperature proportional to α=35” stated in Musiques formelles. Pre-compositional applications are completed by a set of three very detailed graphic tables, through which a wider range of speeds is assigned anew to individual instruments. Due to the composer’s musical intentions, a number of theoretical data are revised. Anticipating the graphic score, creative theoretical reasoning that leads to speed distributions constitutes the scientific matrix of the work, which is bridged with the musical matrix by the application of theoretical results. Xenakis’s theoretical reasoning might be regarded as pure creation proportionally equivalent to composition itself.